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Statistical Analysis of HDD Failure ¶

Matthew unrue, spring 2020 ¶, western govenors university msda capstone ¶, website version note: ¶.

This notebook is so large and works with so much that data that it was run in multiple settings with the kernel reset for memory management each time. As such, the code cell blocks have execution numbers that are not perfectly in order. Though these do not match up perfectly in this version, the code was and should only be excecuted from top to bottom.

Additional Resources: ¶

The 5-page project Executive Summary can be found here . The reveal.js based multimedia presentation notes can be found here . The 87-page report write-up of this project can be found here .

Table of Contents: ¶

Introduction ¶

What factors indicate impending hard disk drive failure ¶, h0: study factors do not significantly indicate impending hard disk failure. ¶, h1: study factors do significantly indicate impending hard disk failure. ¶, context ¶.

Data helps businesses solve problems, make better decisions, and understand consumers, but a lot of data needs to be stored and available to enable these benefits. Hard drive failure is the most common form of data loss, which is one of the most impactful problems that businesses can experience today as simple drive recovery can cost up to $7,500 per drive (Painchaud, 2018). For cloud-based data centers, keeping multitudes of businesses’ data intact for their own operations is crucial. Being able to predict which hard drives are at the highest risk of failure based on understanding of the combinations of routine diagnostics test results is an ideal solution to backup and replace failing drives before the data is lost.

Data ¶

The dataset used is Backblaze’s 4th quarter data from 2019 (Backblaze, 2020). All of the needed data is contained within the .zip file that Backblaze provides to the public as .csv files split by day.

The dataset contains .csv files for each day of its corresponding quarter, from 2019-10-01 to 2019-12-31. As an example, the subsection of the dataset for 2019-10-01 contains 115,259 rows of data. However, as this data contains recorded readings from a live data center, the number of hard drives and thus rows, changed daily as failed drives were taken out and new drives were installed. The 129 column attributes are Date, Serial Number, Model Number, Capacity, Failure, 62 Self-Monitoring, Analysis and Reporting Technology (SMART) test results, and 62 normalized values of the SMART test values. The Failure attribute is the dependent variable of this study and is a qualitative binary categorical variable. The Date, Serial Number, and Model are nominal qualitative independent variables. Finally, and the SMART value columns are continuous quantitative independent variables.

As stated in Backblaze’s Hard Drive Data and Stats page (Backblaze, n.d.), this dataset is free for any use as long as Backblaze is cited as the data source, that users accept that they are solely responsible for how the data is used, and that the data cannot be sold to anybody as it publicly available.

Data Analytics Tools and Techniques ¶

Python, pandas, and the scikit-learn stack are extensively used for the loading, tidying, manipulation, and analysis of the datasets. PyTorch is used for all neural network related tasks of the analysis and model production. Matplotlib and seaborn are used to create charts and graphics for analysis and presentation of project findings. A needed algorithm, namely Fisher's Exact test for contingency tables greater than 2x2 dimensions, is unavailable in the scikit-learn ecosystem, and R.stats is used for this by using rpy2 to run the R code by embedding it in the Python process. Prince is used for factor analysis, and imbalanced-learn is used for the implementation of SMOTE.

Like R and unlike SAS, all of these packages are easily available, free, and open-source with Python. These methods have been chosen over R for ease of explanation, as Python code is often understood more readily than R, and because of the potential of integrating this project directly into a program or software for future use. While R is highly specialized for statistics and mathematics, Python is a general-purpose programming language with specialized libraries for the needed tools, and this facilitates project expansion in the future.

Synthetic Minority Over-Sampling Technique (SMOTE) is used specifically to handle the imbalanced classes for training and testing splits. PCA is used for dimensionality reduction. Predictor variables are examined through correlation coefficients and Fisher's exact test, as well as graphed univariate and bivariate distributions. A logistic regression model and a decision tree model are examined along with the results of the PCA to find predictor variables as well. For building a predictive model for future use, the logistic regression model, a random forest ensemble model, and neural networks are compared to determine which can produce the most useful model.

As HDD failure is an extremely rare event, the dependent variable class is extremely imbalanced and failing to control for the imbalance through techniques like boosting or oversampling would lead to ineffective models. As the dependent variable is a Boolean value, this task is a binary classification task. Logistic regression is an ideal predictive model for binary classification tasks that gives a probability for classification while also having a simplistic interpretation of coefficients that can be used for feature selection. Decision trees are also simple to understand and work well for classification tasks. Given the complexity of the various fields in the dataset, a more complicated model may work better for predictive power. Random forests and neural networks work very well for classification tasks under these circumstances.

Project Outcomes ¶

The key project outcomes are a deep understanding of the risk of hard drive failure based on the results of SMART test values regardless of manufacturer and predictive models that will be able to flag hard drives that are at high risk of failing. The understanding of the risk of failure based on test values will empower better business decisions by optimizing the choice of storage used based on projected lifetime. The predictive models will allow the business to proactively backup data from storage onto new storage devices before failure while also allowing hard drives to continue working closer to their end of life, minimizing waste from constantly replacing hard drives before it is needed. The combination of these two products will also enable the future creation of a more automated system that protects data from hard drive failure.

Dataset Preparation ¶

The dataset provided by Backblaze is made up of 92 .csv files, 1 for each day in the 2019 4th quarter, totaling 3.13GB of text data. As hard drive failure is an extremely rare event, all of these days will need to be considered together in order to have enough failures to draw conclusions. The project begins by combining all parts of the dataset from their .csv files into a single file.

Out of 10,991,209 hard drive days, there were only 678 failures, which gives a failure rate of 0.006169%.

Weiss (2013) defined the imbalance ratio as the ratio between majority and minority classes with a modestly imbalanced dataset having an imbalance ratio of 10:1, and extremely imbalanced datasets as having an imbalance ratio of 1000:1 or greater (pg. 15). This dataset has an imbalance ratio of approximately 16,210:1 and as such will require very careful cultivation in order for any predictive model to successfully learn from. The rarity of the positive failure cases is also the reason that the entire 4th quarter dataset is required.

Unfortunately, this combined file requires too much memory to load all at once for current hardware restraints. It needs 13.5GB for just the data, not including the memory needed for the OS and other software, nor memory for calculations.

As this dataset contains both raw and normalized values for all of the SMART values, a simple way to deal with the memory issues is to divide the dataset into a raw form and a normalized form.

Data Tidying ¶

The considerably smaller raw value subset of data is the main dataset of this project. As with nearly all real-world datasets, this one needs considerable cleaning and tidying in order to use for analysis.

30 rows × 68 columns

All SMART test columns have null values in some rows. The dataset notes state that this comes from differing manufacturer's standards despite the standardized nature of SMART tests.

Deriving the manufacturer from the model column will allow the dataset to be easily divided by manufacturer.

The "DELLBOSS VD" model value seems the be the only value potentially out of place.

60 rows × 68 columns

None of the SMART values exist for this hard drive model, but 60 of the drives have this model value. Additionally, no failures for this model exist in the dataset. Any row with this model value should be removed from the training data before any predictive analysis. Some searching online leads to the belief that it may be a RAID controller. ( https://www.dell.com/support/manuals/au/en/aubsd1/boss-s-1/boss_s1_ug_publication/overview?guid=guid-b20ef25b-b7e3-40f2-b7cd-e497358cd10a&lang=en-us )

0 rows × 68 columns

Additionally the "Seagate SSD" model seems to be missing information. Like the "DELLBOSS VD" model rows, this one also does not have any failures and will need to be removed before predictive analysis is performed.

96 rows × 68 columns

The rows not appropriate for analysis are deleted.

5 rows × 69 columns

Dtype Conversion ¶

Given the size of the dataset, a few minor changes to the columns may free up a considerable amount of memory. The date and capacity_bytes columns are two easy places to improve.

Here we can see that 1108 drive days have an error value rather than their actual capacity. These rows may need to be removed, but may also be an excellent signal for a failing drive.

Unfortunately, all drives experiencing this error do not fail and this can introduce problems in the final model. As it only affects 0.01% of the dataset, removing the affected rows seems best.

The capacity_bytes column is converted from bytes to terabytes to condense the information on disk.

5 rows × 70 columns

Raw Data Univariate Distributions ¶

With these things finished, the univariate distributions can be examined to gain a better sense of the data.

The first column, date shows some sort of testing or operational failure on November 5th.

Drive capacities are mostly 4, 8, and 12 TB, likely coinciding with large investments in new drives for the datacenter and possibly alongside the price lowering of specific models.

The manufacturer of the most drives in this dataset is Seagate at 72.59%. HGST is the second highest at 24.24%. Western Digital is the least represented manufacturer in the dataset with only 0.23%, but as HGST was acquired by Western Digital in 2012 (Sanders, 2018), the drives in this dataset will likely be quite similar between the two manufacturers given the seven-year timespan between then and the time of dataset recording and creation. Finally, Toshiba is the other manufacturer, with 2.94% of the dataset. This amount is quite low and may make it difficult to accurately predict their drives in comparison.

The SMART values vary greatly from the number of different types of drives that exist in this dataset. Before the columns can be graphed appropriately, the NaN/null values need to be examined. It's most likely that the missing data is most related to the hard drive's manufacturer or model.

Every single SMART figure column has null values.

The count row is equivalent to the number of non-null values. If a column has a count of 0, every single value in it is NaN or null, and should be deleted.

smart_13_raw, smart_15_raw, smart_179_raw, smart_181_raw, smart_182_raw, smart_201_raw, smart_250_raw, smart_251_raw, smart_252_raw, and smart_255_raw are all empty in this dataset, as all rows have NaN values in these columns.

Unfortunately, this operation takes too much memory to do in this manner. Each column will have to be graphed separately and then the graphs combined into a single graphic for the same effect.

5 rows × 59 columns

NaN Value Management ¶

With some dataset tidying complete, the final major dataset adjustments that need to be made before analysis can be performed is that the NaN values need dealt with. The rows or columns with them can be removed, or they can be filled in through interpolation or estimation.

The first five mostly complete columns all have two NaNs, which are the result of two rows that have no raw smart values at all. Both drives failed, making them quite important for predicting future failure. However, the lack of data makes them useless for predicting future failure in their current form.

The most likely scenario is that both drives failed just before the diagnostics were collected. As such, these two rows will be deleted and their associated row for the date before their currently marked failures will be updated to have failed that day.

2 rows × 59 columns

1 rows × 59 columns

The next section of columns all have 8792 rows with NaNs, ignoring the 2 rows just removed. Coincidentally, all of these columns share the same problematic rows.

8792 rows × 59 columns

This subset of drives are all manfactured by Seagate, and are 3 size variations of the same model line. There is not an updated model from this line in this dataset to interpolate values from.

Interpolating mean values from the same manufacturer, Seagate, and the models' respective capacity_TB categories would be a good way to estimate the missing values if enough data exists.

Additionally, creating a boolean column to flag interpolated data as missing may help the predictive models account for it.

smart_3_raw ¶

For the smart_3_raw data, the median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_4_raw ¶

For the smart_4_raw data, the mean for the manufacturer and drive capacity will be used for the second model. The mean for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_5_raw ¶

For the smart_5_raw data, the median for the manufacturer and drive capacity will be used for the second model. The median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_7_raw ¶

For the smart_7_raw data, the median for the manufacturer and drive capacity will be used for the second model. The median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_10_raw ¶

For the smart_10_raw data, the median for the manufacturer will be used to fill the NaN values.

smart_197_raw ¶

For the smart_197_raw data, the median for the manufacturer and drive capacity will be used for the second model. The median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_198_raw ¶

For the smart_198_raw data, the median for the manufacturer and drive capacity will be used for the second model. The median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_199_raw ¶

For the smart_199_raw data, the median for the manufacturer and drive capacity will be used for the second model. The median for the manufacturer without regard for the drive capacity will be used for the first and third model of drive, as there are no appropriate rows with values to interpolate from.

smart_193_raw and smart_225_raw ¶

The smart_193_raw column is a different problem than the last group of columns. This group has 53985 rows with NaN values, which is still low enough in this large dataset to interpolate values without majorly ill effects, but still requires caution.

An important note here is that some manufacturers use different SMART attributes to represent the same information. Most Seagate and some Western Digital and Hitachi drives actually use 225 rather than 193 to store the Load/Unload Cycle Count value (Acronis, Knowledge Base 9128; Acronis, Knowledge Base 9152). We can see here that no row has both 193 and 225 values.

53985 rows × 59 columns

53985 rows × 2 columns

The only rows that do not have either value are the exact same rows as the last group. These will need interpolated if the rows are to be kept. The 45193 other rows can be filled by combining the two columns that represent the same information.

8792 rows × 2 columns

The smart_193_raw and smart_225_raw columns will be combined into a new smart_193_225 column and then the remaining values filled as in previous columns.

5 rows × 58 columns

Now that the two columns have been merged, the same process of interpolation by model and capacity can be used on the remaining group.

The remaining columns to examine all have over 2 million NaN value rows each. This level of missing data causes interpolation to skew results far more than the previous groups' levels of missing data. The following grouping of columns have at least 70% of their values.

smart_240_raw, smart_241_raw, and smart_242_raw ¶

Notably, none of the HGST drives have a value for the smart_240_raw column. Additionally, the drives that are missing the smart_241_raw data are also likely the drives missing the smart_242_raw data.

Seagate drives have enough filled values to use and Toshiba drives have no missing values, but the HGST and Western Digital drives do not have enough values to interpolate from. As such, all missing values will be filled in with the mean.

smart_187_raw, smart_188_raw, and smart_190_raw ¶

The group of the smart_187_raw, smart_188_raw, and smart_190_raw columns are divided by manufacturer, with all Seagate drives having the values and none of the other drive manufacturers having the values.

Given the column distributions, the smart_187_raw and smart_188_raw NaNs will be filled with the medians, and the smart_190_raw NaNs will be filled with the mean.

Memory Management and Reloading Checkpoint ¶

The remaining columns ¶.

These remaining columns have over 30% of their values missing, and an individualized approach will be taken with each of them. In some cases, categories of existing values may be helpful to preserve the potential for information with NaNs being their own category.

smart_195_raw ¶

This column only has values in a single manufacturer's drives, and even then only 77% of them. There appears to be virtually no difference in the column's distribution by failure status. Filling in NaNs with this information would only result in collinearity between the column and the manufacturer column, so it will be dropped from the dataframe.

5 rows × 57 columns

smart_191_raw ¶

This column is not split along manufacturer lines like many others, but still has a large percentage of missing values. A categorical column smart_191_cat will be created with the following categories and values.

The original smart_191_raw column will then be dropped.

smart_184_raw ¶

This column very rarely has any value other than 0 when it is available. However, whenever it is available and not 0, it has a disproportionate ratio of failures to nonfailures, making it a very useful measure for predicting failure. A categorical column smart_184_cat will be created with the following categories and values.

The original smart_184_raw column will then be dropped.

smart_189_raw ¶

This column only has values in a single manufacturer's drives, and even then only 38% of them. There is also little correlation between this column and the failure rate. Filling in NaNs with this information could result in collinearity between the column and the manufacturer column as well, so it will be dropped from the dataframe without a category column.

5 rows × 56 columns

smart_200_raw ¶

This column is not entirely split along manufacturer lines like many others, but still has a large percentage of missing values. Given the reasonably large correlation between a higher value and a higher failure rate, a categorical column smart_200_cat will be created with the following categories and values.

The original smart_200_raw column will then be dropped.

smart_196_raw ¶

This column is not split along manufacturer lines whatsoever, but still has a large percentage of missing values. Given the reasonably large correlation between a higher value and a higher failure rate, a categorical column smart_196_cat will be created with the following categories and values.

The original smart_196_raw column will then be dropped.

smart_8_raw ¶

This column is not strongly split along manufacturer lines, but still has a large percentage of missing values. Given the reasonably large negative correlation between a higher value and failure rate, a categorical column smart_8_cat will be created with the following categories and values.

The original smart_8_raw column will then be dropped.

smart_2_raw ¶

This column is not strongly split along manufacturer lines, but still has a large percentage of missing values. Given the reasonably large negative correlation between a higher value and failure rate, a categorical column smart_2_cat will be created with the following categories and values.

The original smart_2_raw column will then be dropped.

smart_183_raw ¶

This column only has values in a single manufacturer's drives, and even then only 23% of them. There is also little correlation between this column and the failure rate. Filling in NaNs with this information could result in collinearity between the column and the manufacturer column as well, so it will be dropped from the dataframe without a category column.

5 rows × 55 columns

smart_22_raw ¶

This column only has values in a single manufacturer's drives, as it is an indication of helium levels encased in certain HGST drives (Klein, 2015). Given this, it would make no sense to fill this column's NaN values in rows of drives from other manufacturers. Beyond that, the dataset does not have any failures with abnormal levels, making this column potentially a negative impact to the real-world effectiveness of a predictive model. Given this risk, the risk of collinearity with the manufacturer column, and the low correlation of this column and the failure rate, this column will be dropped from the dataframe without a category column for the simplification of the models.

5 rows × 54 columns

smart_223_raw ¶

This column is not strongly split along manufacturer lines, but still has a large percentage of missing values. Given the reasonably large negative correlation between a higher value and failure rate, a categorical column smart_223_cat will be created with the following categories and values.

The original smart_223_raw column will then be dropped.

smart_18_raw ¶

This column is not only missing 97% of its values, it also has no variance whatsoever, making it useless for analysis.

5 rows × 53 columns

smart_224_raw ¶

5 rows × 52 columns

smart_220_raw ¶

This column is entirely split along manufacturer lines and has a large percentage of missing values, but it seems to be one of the few predictors available for Toshiba drives. Given the relatively large negative correlation between a higher value and failure rate, a categorical column smart_220_cat will be created with the following categories and values.

The original smart_220_raw column will then be dropped.

smart_222_raw ¶

Although only available on the Toshiba drives, this is the highest correlation to failure rates yet. A categorical column smart_222_cat will be created with the following categories and values.

The original smart_222_raw column will then be dropped.

smart_226_raw ¶

Although only available on the Toshiba drives, this is the highest negative correlation to failure rates yet. A categorical column smart_226_cat will be created with the following categories and values.

The original smart_226_raw column will then be dropped.

smart_23_raw ¶

This column is not only missing 98% of its values, it also has no variance whatsoever, making it useless for analysis.

5 rows × 51 columns

smart_24_raw ¶

5 rows × 50 columns

smart_11_raw ¶

Although only available on 0.64% of drives, this is the highest correlation to failure rates yet. A categorical column smart_11_cat will be created with the following categories and values.

The original smart_11_raw column will then be dropped.

smart_254_raw ¶

This column is not only missing 99.75% of its values, it also has no variance whatsoever, making it useless for analysis.

5 rows × 49 columns

smart_235_raw ¶

This column represents an interesting report, in that the first 3 bytes of it is the drive's good block count, while the last 2 bytes is the drive's bad block count, but this column is missing 99.92% of its values, making it useless for this type of predictive analysis.

5 rows × 48 columns

smart_233_raw ¶

No failures exist in the drives that have any value for this column, and it is also missing 99.92% of its values, making it useless for analysis.

0 rows × 48 columns

5 rows × 47 columns

smart_232_raw ¶

0 rows × 47 columns

5 rows × 46 columns

smart_168_raw ¶

0 rows × 46 columns

5 rows × 45 columns

smart_170_raw ¶

0 rows × 45 columns

5 rows × 44 columns

smart_218_raw ¶

0 rows × 44 columns

5 rows × 43 columns

smart_174_raw ¶

0 rows × 43 columns

5 rows × 42 columns

smart_16_raw ¶

0 rows × 42 columns

5 rows × 41 columns

smart_17_raw ¶

0 rows × 41 columns

5 rows × 40 columns

smart_173_raw ¶

0 rows × 40 columns

5 rows × 39 columns

smart_231_raw ¶

0 rows × 39 columns

5 rows × 38 columns

smart_177_raw ¶

0 rows × 38 columns

5 rows × 37 columns

Analysis of Potential Predictors ¶

With all NaN values interpolated or their columns removed, correlations can be determined between the columns.

22 rows × 22 columns

A few of the columns' relations will need to be examined well based on these correlation coefficients.

A prominent feature is smart_9_raw as the column with the most extreme correlations with other columns, which is understandable given that SMART attribute 9 represents the total count of hours the drive has been in a power-on state (Acronis, Knowledge Base 9109). Most other issues worth measuring are likely correlated with the drive age and amount of operation. This column may also be a powerful predictor within predictive models as an older drive is more likely to wear down to failure suddenly than a newer drive in general even if other values are not present. Even if other predictors of failure are present in an instance, a drive with an average or lower smart_9_raw value may represent a drive that will fail far sooner than the average length of time to failure.

smart_240_raw also has quite high correlations with other independent variables.

smart_197_raw and smart_198_raw have a nearly perfect degree of collinearity with each other and little in comparison with any other column. smart_198_raw will be dropped as it has a lower correlation with the dependent variable failure.

Finally, smart_190_raw and smart_194_raw have a very high degree of collinearity with each other and little in comparison with any other column. One likely needs removed.

The dataset may be large enough to not need to worry about the multicollinearity affecting the predictive power of the models, but the redundancy of information may skew the results.

For potential predictors for failure, smart_5_raw and smart_197_raw have the highest positive correlations with failure, at 4.4% and 2.7%. SMART attribute 5 is the reallocated sectors count of drives, which triggers when a read, write, or verification error occurs (Acronis, Knowledge Base 9105). SMART attribute 197 is the current pending sector count, which is the count of unstable sectors that are awaiting remapping (Acronis, Knowledge Base 9133). This value decreases as sectors are remapped, but the value would remain consistently high if these sectors are unable to be remapped. Both columns make complete sense as the highest correlation with failure and will likely be the most important predictor variables for HDD failure.

manufacturer ¶

Model ¶.

The model column will ultimately be dropped even after all of the work that went into cleaning its data. The large amount of categories in it substantially adds complexity to the model while not improving enough. The manufacturer column, while less specific, contains all of the same variation with only four categories. Additionally, many of the models do not have a single failure, and even more have only thousands of hard drive days that they represent. Leaving the column in for predictive modeling and analysis will only hurt the overall results, and as such, is removed.

capacity_TB ¶

Smart_191_cat ¶.

This column has the highest p-value out of all of the category columns. While still statistically significant, this is likely from the size of the dataset and not out of pure correlation. smart_191_cat is not likely to be a good predictor variable.

smart_184_cat ¶

With a p-value of 0.0, this is likely the strongest relation to failure in the dataset.

smart_200_cat ¶

Smart_196_cat ¶, smart_8_cat ¶, smart_2_cat ¶, smart_223_cat ¶, smart_220_cat ¶, smart_222_cat ¶, smart_226_cat ¶, smart_11_cat ¶, dataset preparation for model creation ¶.

To begin performing factor analysis, the dataset will need to be prepared through standardization and normalization, as well as the test, train, and validation splits. Doing these before the PCA ensures that no data is contaminated with the influence of the testing and validation data.

Dataset Splitting: Train, Test, and Validation ¶

The first split is 80% Train and 20% Test, stratified on the y_df / failure series.

Verify the stratified splitting.

Note that while the ratio is not exact, it is the closest possible.

The second split is 87.5% Train and 12.5% Validation, stratified on the y_df / failure series, to result in 70% Train and 10% Validation overall.

Continuous Variable Standardization ¶

A scaler fit to the training data is created to standardize the continuous columns for model training. This avoids any contamination of the training data by ensuring that the test and validation datasets do not influence the training data at all.

This fits the scaler to the continuous columns of the training data. The fit scaler will then be used to scale the testing and validation datasets.

A mean as close to zero as possible given the dataset and a standard deviation of 1 is a successful standardization.

PCA and MCA ¶

The eigenvalues and explained inertia were used to create a scree plot, and this plot is then used alongside the cumulative inertia to determine that 13 principal components an appropriate amount of dimensionality reduction to use as these components made up 82.37% of the inertia of the dataset in only 13 out of the 20, or 65%, of the total components.

PCA as a form of dimensionality reduction ensures that as little information, in the form of inertia, is lost as possible for the given number of dimensions reduced. As this dataset is quite large, any amount of dimensionality reduction will greatly affect the speed and chance of proper convergence in the predictive models to come. The result is reducing of the data by 35% while only losing 17.63% of the information, a 2-for-1 trade.

Training set PCA transformation ¶

7682577 rows × 13 columns

5 rows × 25 columns

Test set PCA transformation ¶

2195023 rows × 13 columns

Validation set PCA transformation ¶

1097511 rows × 13 columns

To begin doing MCA, the categorical columns need converted to boolean encoding columns.

While Factor Analysis of Mixed Data (FAMD) would have been ideal for dimensionality reduction, the current hardware requirements and software availability do not allow for it with such a large dataset.

Why SMOTE (Synthetic Minority Oversampling Technique) is Needed ¶

Traditional training fails as hard drive failure is an extremely rare occurence. The model learns to only predict non-failure, making it useless for actually predicting failure. This is why a combination of undersampling the non-failures and oversampling the failures will improve the training and production of the predictive models.

SMOTE ¶

Model creation ¶, logistic regression with smote ¶, lbfgs solver logistic regression ¶, decision tree ¶, random forest ensemble ¶, random forest ensemble with class weights ¶.

In an attempt to train the ensemble in a way that prioritizes the true negative, or actual failure cases, this version of the random forest weights failures as twice as important as non-failures.

Compared to the unweighted Random Forest ensemble, this weighted ensemble gains another 6 true negative classifications for a true negative rate of 40% rather than 36%, but also gains 40,687 false positive classifications, for 0.028%, instead of 0.0097% false positives.

Neural Networks ¶

PyTorch requires the boolean values to be converted to floating point, so these dtypes will be changed before the neural network is defined.

Neural Network 1 ¶

While it may eventually improve with enough training, it's most likely that this architecture of neural network is too simple for the problem at hand. A more complex one will be built next.

Neural Network 2 ¶

It may seem quite odd that the testing loss is consistently lower than the training loss. In this case, it's quite likely the the sheer size of the training set causes this to occur. The model is constantly improving every training batch and the training loss is calculated from the entire epoch. The testing loss is calculated after the entire epoch of batches have all affected the model for the better.

While 50 epochs were originally planned, the test loss consistently decreases even at the 50th epoch. Additionally, when compared to the other models, this neural network has a very high amount of true negative predictions and a moderately low amount of false positive predictions. Additional training may result in a model that outperforms even the LBFGS solved logistic regression model for this task.

Validation Results ¶

Conclusions ¶.

Table 1 HDD Failure Predictive Model Testing Results

The Project Limitations ¶

A few limitations of this project exist. First, a very large amount of the dataset was made up of missing values. A second limitation that deserves caution is that the ratios of drives made by each manufacturer in the dataset is very imbalanced. No assumptions about value or reliability of the four manufacturers included in the dataset should be made from this data. A third limitation is that the dataset was extremely imbalanced in terms of the minority (failure) and majority (non-failure) classes. Though SMOTE succeeded exceptionally well at allowing predictive models to learn from the imbalanced data, it does introduce bias as the synthetically created instances of the minority classes overrepresent their information in the analysis. Finally, working computer memory was a great limitation throughout the project as the dataset is so large. This limitation prevented factor analysis of mixed data from being performed and PCA had to be selected as the alternative.

Actions Proposed and Expected Benefits ¶

It is highly recommended that either the logistic regression model or the more complex DNN model is added to the daily HDD diagnostics checks and backup procedure pipeline. The complex DNN will successfully flag 71.3% of drives expected to fail that day and the logistic regression 64%, allowing for total backup and retirement of the drive before the failure occurs. Do note that while more sensitive to detecting failure, the DNN does have a higher false positive rate, at 6.36%, than the more conservative logistic regression at 2.68%. Until this can be completed, special care should be given to drives with higher values of SMART attributes 5, 197, and 9 to reduce data loss and complications arising from the events of HDD failure.

Once implemented, an ensemble approach between the two should be tested to further reduce the false positive rate. Furthermore, additional research is warranted beyond the scope and limitations of the project. Taking an RNN approach to the data tidying and predictive modeling will almost certainly improve the results quite significantly, as they are specifically designed for time-series data such as this.

References ¶

Acronis. Knowledge Base 9105. S.M.A.R.T. Attribute: Reallocated Sectors Count | Knowledge Base. https://kb.acronis.com/content/9105 .

Acronis. Knowledge Base 9109. S.M.A.R.T. Attribute: Power-On Hours (POH) | Knowledge Base. https://kb.acronis.com/content/9109 .

Acronis. Knowledge Base 9128. S.M.A.R.T. Attribute: Load Cycle Count; Load/Unload Cycle Count | Knowledge Base. https://kb.acronis.com/content/9128 .

Acronis. Knowledge Base 9133. S.M.A.R.T. Attribute: Current Pending Sector Count | Knowledge Base. https://kb.acronis.com/content/9133 .

Acronis. Knowledge Base 9152. S.M.A.R.T. Attribute: Load/Unload Cycle Count | Knowledge Base. https://kb.acronis.com/content/9152 .

Backblaze. (2020). data_Q4_2019. San Mateo, CA; Backblaze. Klein, A. (2015, April 16). SMART Hard Drive Attributes: SMART 22 is a Gas Gas Gas. Backblaze Blog | Cloud Storage & Cloud Backup. https://www.backblaze.com/blog/smart-22-is-a-gas-gas-gas/ .

Painchaud, A. (2018, October 31). 8 Reasons on How Data Loss Can Negatively Impact Your Bussiness. https://www.sherweb.com/blog/security/statistics-on-data-loss/ .

Sanders, J. (2018, November 13). Western Digital spins down HGST and Tegile brands in hard disk market shuffle. TechRepublic. https://www.techrepublic.com/article/western-digital-spins-down-hgst-and-tegile-brands-in-hard-disk-market-shuffle/ .

Weiss, G. M. (2013). Foundations of Imbalanced Learning. Imbalanced Learning, 13–41. https://doi.org/10.1002/9781118646106.ch2

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The current Internet-available world opens many doors and eliminates borders. It is now possible to get a good education online without going anywhere. For some students, this matter is of extreme importance if they may allow themselves to study online only.

Western Governors University should be emphasized among all online institutions that provide distance learning. It is possible to be engaged in studies of English, pedagogy, nursing, health system management, social science, finance, and accounting. For completing any degree program, each student should prepare a WGU capstone project. If you are looking through this page, you are probably one of the students who should complete this project too.

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Introductory Points about What Is a Capstone WGU?

If you have faced this project for the first time, you may wonder what is a capstone WGU? This is paperwork in certain fields dedicated to investigating its up-to-date matters. This work is aimed at exploring this subject and illustrating knowledge a student has gained after the studies. Another aspect that is assessed and appreciated while writing is the students’ ability to contribute to a certain field he/she works with.

So, this project checks and illustrates student’s abilities of research, analytical, critical thinking, and writing work. It requires special and precise preparation, and we have got good tips for that.

Basic WGU Capstone Guidelines

If you want to get workable and tested tips on how to make this project successful – one that can ensure good grades to you, our professionals have prepared for you such tips and pieces of advice:

If these WGU capstone guidelines are not too helpful for making your paper at the moment or you lack inspiration, our professionals are always ready to come and help you with creating a good capstone project or any other project that you need. And we also have tested tips on how to pass this project.

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Writing this project is one point; you may also wonder how to pass WGU capstone. There are simple steps to gaining your confidence. Only prepare yourself well and make brief notes on the subject of your paper. Making a WGU capstone presentation also may be required; make sure it is structured well. Relying on your outline is very useful in this case. If you experience difficulties with making your presentation, professional helpers may assist you with that.

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WGU MBA Capstone: Steps and Tips for Making It

WGU MBA capstone is a compulsory project that students of the Online College of Business should complete to prove they are ready for performing tasks in line with MBA requirements. This project checks the background students have gained, their ability of comprehensive research, and the analytical skills they have.

Among the aims this project has the following are the most important:

Making this paper is focused on searching well on the matter, defining the main peculiarities of any investigated process, developing independent judgments and findings, and writing about such well too. If preparing this project appears to be too complicated for many reasons, you may always ask professionals to come and help you solve that task easily.

Making a Winning WGU Business Management Capstone

WGU business management capstone is another variation of this considered project that is focused mostly on the management issues in business organizations. This paper may be focused on managerial tasks related to financial, human, or material resources. For instance, you may be required to develop a WGU capstone business plan with an emphasis on managerial tasks. In WGU accounting capstone examples, it is necessary to focus on strategies for managing financial resources.

In any case, the shortest strategy for making this project winning is presenting independent findings and suggestions on the investigated matter. Such should be practically workable, and that should be obvious for your future reviewers. Think from their perspective to increase your chances for truly workable findings and high grades from this work.

Do You Need More Help to Complete a Task You Have?

Many questions may arise while doing this project. Where to find credible sources? How develop the exact findings to make this paper winning? Where to find WGU MBA capstone project ideas? How to pass WGU MBA capstone? What is a workable WGU capstone submittal form? And the most important – how to reach WGU capstone excellence?

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I was enrolled in a doctorate program, which helped me build a practical career as an applied psychologist. Numerous events clued me in about the current issues relating to children’s and adults’ behavior. I want to share my knowledge with students who are earning the same degree.

When working for international IT companies, I realized I wanted to support future specialists and show them all the diversity of the IT area. Now I assist graduates with their practical case studies in computer sciences and improve their software-developing skills.

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Requirements to WGU MBA Capstone Writing

The programs offered through the university are split into four main schools, each with their own unique offerings and also formal accreditations. These schools are business, teaching, IT and health & nursing. Each school has several distinct programs for bachelor’s and master’s degrees.

As with most universities, each of the schools has its own very specific requirements as to how your document must be laid out and structured. These instructions for writing a capstone paper are clearly laid out, and you must ensure you follow these instructions to the letter if your essay is to be accepted. Mistakes in your formatting cause your article to be rejected and it can be returned to you for revisions. On the whole, you might be expected to provide citations and references within your APA style for the majority of works when you write a WGU capstone.

Steps in Writing

As with all other sections of your education through you may be required to do your WGU capstone project. You have an approval process to undertake as well as numerous forms and stages to go through to ensure you submit a master’s work and it would meet their expectations. There are some differences between programs but the typical process follows this route.

The researches will be reviewed and you will either pass, fail, or have your WGU MBA capstone returned to you for revisions. You will have to do pretty poorly to actually fail, on the whole, you will be given the opportunity to correct any issues with your work and to resubmit. There is face to face review as the programs are wholly done online.

Project Writing Tips

Writing is not an easy task and it is something many students struggle with, especially if they are not used to writing an analysis of this size and complexity. It is always best to use all of the resources are provided for your capstone CSULB such as the many guides and videos spell out what is required of you. Our WGU business management capstone tips will help you to better understand how you should approach writing your task if you want to get the best possible final result:

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Academic level, type of assigment.

Given the difficult time in which we live, the principle of teaching each country changes to match the circumstances. The program and principles of education in the United States are changing in the same way, and at the moment, they are actively using distance learning. The reasons for this are simple: in order to train specialists and not lose economic leadership, the country must take all necessary measures and continue to train specialists. Online learning has become a solution to this problem and is now actively used by some universities and special training courses for specialists.

One of the educational institutions that have made significant progress in learning online is Western Governors University. This university has existed for 24 years and currently offers online training programs in four different specializations: business, pedagogy, information technology, and medicine. A feature of the college is a project that each student carries out after completing their studies. This project is called wgu capstone and is not an easy task for students because in doing it, each student must take stock of what they have learned over the course of the course. 

The wgu capstone project requires the student to tell how exactly he can influence the profession he studied and what success he has already achieved. Each student has the possibility of delaying the writing of the capstone project wgu, but this is strongly discouraged, as this affects the completion of the educational process. One way or another, each student is obliged to write this paper work. But there are times when, for personal reasons, this is not possible. And then the time comes for our professional service.

WGU MBA Capstone: Why Does It Exist and What to Include In It?

Answering the question what is a capstone project wgu, we want to tell you about this issue, as well as about the details of writing this paper work. This project is a final work and shows the student’s knowledge that he acquired in the process of studying at college while studying the business field. 

Teachers are interested in doing this work for you for one simple reason: in this way, they can give a clear assessment of your knowledge and see what perspective you can give in the future. Such a wgu capstone project differs from projects that students perform in other college courses primarily in that:

By creating such paperwork, the future specialist should be well versed in what he is writing and be able to apply the knowledge he has acquired earlier. All new skills that you already possess should be vividly shown in such a project.

How WGU Capstone Business Plan Should Look Like

There is the case when according to wgu business capstone project, students are given the task of creating a business plan. This can be given in order to try the strength of the student and his vision of the future profession. A business plan, in general, draws up for companies at the stage of their creation or when the company plans to introduce new projects for use. 

The business plan helps leaders and all other employees of the company understand the goals and describes in detail the actions that will be taken to achieve them. A business plan is also very often required by companies in order to present themselves at meetings with investors and shareholders. So, for example, unlike the WGU nursing project, this type of work is more accurate and has a large number of calculations. Each wgu capstone project should have a clear structure and consists of: 

So, this is just a short description of the plan, and after reading, you should understand everything—the responsibility and complexity of the process. A large number of numbers are included in this work and this, unfortunately, is often a big problem for completing a training course for students.

Basic Structure of WGU Capstone Project

Let’s talk about the structure of the western governor’s university capstone project. This work, like any other, should be easy to understand, despite the fact that it includes rather a complex terminology. Wgu mba capstone should be divided into title page, the content of the main parts of the project, introduction, main text, conclusion, and references at the end of a project. As we can see, the WGU capstone business plan is not too different from other types of paperwork and has a very typical structure. After collecting all the necessary information, it should not be difficult to divide it into these parts and give a finished look.

How to Measure WGU Nursing Capstone Quality

Like all other papers, wgu capstone evaluates your paperwork against several criteria. These criteria are: 

From task to task, all of the above parameters may differ from each other. Suppose, for any reason, the process of creating a project is not possible for you or is incredibly difficult to complete. In that case, we suggest you use the professional help of our company and place your order for writing a business plan already. You can do this on another page of our website, and our specialists will gladly complete the required task for you, taking into account all standards and criteria. Save yourself from all possible difficulties and problems by starting to work with us.

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